## Linear Operators: Spectral theory |

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Page 915

Hilbert space y and let E

sequence { xn } C H such that H = 2 : = 1 H ( x ; ) , where D ( , ) = sp { { ( T ) If e C (

c ( T ) ) } , and a decreasing sequence { en } of Borel sets such that ( E ( e ) xn ...

Hilbert space y and let E

**denote**its resolution of the identity . Then there exists asequence { xn } C H such that H = 2 : = 1 H ( x ; ) , where D ( , ) = sp { { ( T ) If e C (

c ( T ) ) } , and a decreasing sequence { en } of Borel sets such that ( E ( e ) xn ...

Page 1126

of the closed set C ; we shall

( C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ej , it ...

of the closed set C ; we shall

**denote**this subspace of L , [ 0 , 1 ] by the symbol 1 ,( C ) . Since each projection in the spectral resolution of T and hence each

continuous function of T is a strong limit of linear combinations of the projections

Ej , it ...

Page 1486

In the next few paragraphs t

operator of order n , defined on the interval R = { -00 < t < +00 } . Let t have the

form d Ža ; ( e ) dt j = 0 and suppose that all the coefficients a ; are periodic and

have ...

In the next few paragraphs t

**denotes**a formally self adjoint formal differentialoperator of order n , defined on the interval R = { -00 < t < +00 } . Let t have the

form d Ža ; ( e ) dt j = 0 and suppose that all the coefficients a ; are periodic and

have ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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